The article P. Mason about rubber band

[John Melody]

Hello! Please help me understand the scientific article written by P. Mason. I can't figure out what exactly the u_lambda speed means. On what basis did the integral appear in it? I need the retraction rate of the rubber band during the retraction process. Is that her? Is this the speed of the end of the tape retraction in the process? Or does it mean something else? I need to get the rate of retraction of the end, I don't understand if this is it or if I need to express something else. And why does it depend through an integral on the extent to which the wave has passed or what?

[studiot]

 

 

I am away for the w/e

Try the following articles.

Ogden R W  (1972)  Large deformation isotropic elasticity  - on the correlation of theory and experiment for incompressible rubberlike solids

Proc Royal Soc London  A326  565 - 84

Ogden R W  (1972)  Large deformation isotropic elasticity  - on the correlation of theory and experiment for compressible rubberlike solids

Proc Royal Soc London  A328  567 - 83

[studiot]

OK so I have obtained the original article, which for the benefit of other readers is

Finite Elastic Waves in Rubber

P Mason

Proceedings of the Royal Society of London: Series A, Mathematical and Physical Sciences

March 19th 1963

pages 315 - 330

I agree the diagrams are a bit odd, but

In the first 5 pages Mason clearly describes the meanings of the variables v, u, λ₁ and λ₂ ;

 

It seems that the 'wave' referred to is a single unloading pulse which travels back towards the fixed point faster than the material itself.

On 2/7/2025 at 9:46 PM, John Melody said:

I can't figure out what exactly the u_lambda speed means. On what basis did the integral appear in it? I need the retraction rate of the rubber band during the retraction process. Is that her? Is this the speed of the end of the tape retraction in the process?

Different parts of the rubber are travelling at different speeds. That is how is is contracting.